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A grocer purchased a certain quantity of bananas at a price of $0.50 per 3 pounds. He then sold the entire quantity of bananas at a price of $1.00 per 4 pounds. How many pounds of bananas did the grocer purchase if the total profit from selling the bananas was $10.00?

Answer :

Final answer:

In this mathematical problem of profit calculation, the grocer purchased 120 pounds of bananas to achieve a $10 profit, by buying at $0.50 per 3 pounds and selling at $1.00 per 4 pounds.

Explanation:

The subject of this question is a basic mathematical problem dealing with profit calculation. Let's denote the quantity of bananas the grocer purchased by 'x' pounds. Since the grocer bought the bananas at a price of $0.50 per 3 pounds, the total cost of the bananas is ($0.50/3)*x. He sold the bananas at a price of $1.00 per 4 pounds, so the total revenue from selling the bananas is ($1.00/4)*x.

Since profit is defined as revenue minus cost, we set up the following equation to represent the grocer's profits: ($1.00/4)*x - ($0.50/3)*x = $10. By solving this equation algebraically, we can find the quantity of bananas the grocer purchased:

  1. Multiply the equation through by 12 to remove the denominators, resulting in 3x - 2x = 120.
  2. Simplifying gives x = 120 pounds, meaning the grocer purchased 120 pounds of bananas to achieve a profit of $10.

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Rewritten by : Barada

Answer:

$10.00/($1.00/4 - $0.50/3) =

$10.00/(($3.00 - $2.00)/12) =

$10.00/($1.00/12) =

$10.00(12/$1.00) =

120 pounds of bananas